Some dynamical aspects of the accretion of Uranus and Neptune: The exchange of orbital angular momentum with planetesimals

The final stage of the accretion of Uranus and Neptune is numerically investigated. The four Jovian planets are considered with Jupiter and Saturn assumed to have reached their present sizes, whereas Uranus and Neptune are taken with initial masses 0.2 of their present ones. Allowance is made for the orbital variation of the Jovian planets due to the exchange of angular momentum with interacting bodies (“planetesimals”). Two possible effects that may have contributed to the accretion of Uranus and Neptune are incorporated in our model: (1) an enlarged cross section for accretion of incoming planetesimals due to the presence of extended gaseous envelopes and/or circumplanetary swarms of bodies; and (2) intermediate protoplanets in mid-range orbits between the Jovian planets. Significant radial displacements are found for Uranus and Neptune during their accretion and scattering of planetesimals. The orbital angular momentum budgets of Neptune, Uranus, and Saturn turn out to be positive; i.e., they on average gain orbital angular momentum in their interactions with planetesimals and hence they are displaced outwardly. Instead, Jupiter as the main ejector of bodies loses orbital angular momentum so it moves sunward. The gravitational stirring of planetesimals caused by the introduction of intermediate protoplanets has the effect that additional solid matter is injected into the accretion zones of Uranus and Neptune. For moderate enlargements of the radius of the accretion cross section (2–4 times), the accretion time scale of Uranus and Neptune are found to be a few 10⁸ years and the initial amount of solid material required to form them of a few times their present masses. Given the crucial role played by the size of the accretion cross section, questions as to when Uranus and Neptune acquired their gaseous envelopes, when the envelopes collapsed onto the solid cores, and how massive they were are essential in defining the efficiency and time scale of accretion of the two outer Jovian planets.     

Theoretical predictions of deuterium abundances in the Jovian planets

Using current concepts for the origin of the Jovian planets and current constraints on their interior structure, we argue that the presence of large amounts of “ice” (H₂O, CH₄, and NH₃) in Uranus and Neptune indicates temperatures low enough to condense these species at the time Uranus and Neptune formed. Yet such low temperatures imply orders-of-magnetude fractionation effects for deuterium into the “ice” component if isotopic equilibration can occur. Our models thus imply that Uranus and Neptune should have a D/H ratio at least four times primordial, contrary to observation for Uranus. We find that the Jovian and Saturnian D/H should be close to primordial regardless of formation scenario. The Uranus anomaly could indicate that there was a strong initial radial gradient in D/H in the primordial solar nebula, or that Uranus is so inactive that no significant mixing of its interior has occurred over the age of the solar system. Observation of Neptune's atmospheric D/H may help to resolve the problem.     

Dynamical evolution of a cometary swarm in the outer planetary region

The dynamical evolution of bodies under the gravitational influence of the accreting proto-Uranus and proto-Neptune is investigated. The main aim of this study is to analyze the interrelations between the accretion of Uranus and Neptune with other processes of cosmological importance as, for example, the formation of a cometary reservoir from bodies placed into near-parabolic orbits by planetary perturbations and the scattering of bodies to the region of the terrestrial planets. Starting with a mass ratio (initial mass/present mass) of 0.1, Uranus and Neptune acquire masses close to their present ones in a time scale of 10⁸ years. Neptune is found to be the most important contributor of comets to the cometary reservoir. The time scale of bodies scattered by Neptune to reach near-parabolic orbits (semimajor axes a > 10⁴ AU)is about 10⁹ years. The contribution of Uranus was partially inhibited because a large part of the residual bodies of its accretion zone fell under the strong gravitational influence of Jupiter and Saturn. A significant fraction of the bodies dispersed by Uranus and Neptune reached the region of the terrestrial planets in a time scale of some 10⁸ years.     

Comparative thermal evolution of Uranus and Neptune

We extend a Jovian convective-cooling model to Uranus and Neptune. The model assumes that efficient interior convection prevails, so that escape of interior heat is governed by the radiative properties of the atmosphere. A comparison of the thermal evolution of Uranus and Neptune indicates that the larger amount of solar radiation absorbed in Uranus' atmosphere tends to differentially suppress the escape of interior heat. The model is shown to be consistent with recent infrared observations of the thermal balance of Uranus and Neptune, and with the presumed age of these planets.     

Uranus and Neptune interior models

This paper is concerned with the interior structure of Uranus and Neptune. Our approach is three-fold. First, a set of three-layer models for both Uranus and Neptune are constructed using a method similar to that used in the study of the terrestrial planets. The variations of the mass density (s) and flattening e(s) with fractional mean radius s for two representative models of Uranus and Neptune are calculated. The results are tabulated. A comparison of these models shows that these two planets are probably very similar to each other in their basic dynamical features. Such similarity is very seldom seen in our solar system. Secondly, we check the conformance between the theoretical results and observational data for the two planets. And thirdly, the 6th degree Stokes zonal parameters for Uranus and for Neptune are predicted, based on the interior models put forward in this paper.     

The web of three-planet resonances in the outer Solar System: II. A source of orbital instability for Uranus and Neptune

The motion of the giant planets from Jupiter to Neptune is chaotic with Lyapunov time of approximately 10 Myr. A recent theory explains the presence of this chaos with three-planet mean-motion resonances, i.e. resonances among the orbital periods of at least three planets. We find that the distribution of these resonances with respect to the semi-major axes of all the planets is compatible with orbital instability. In particular, they overlap in a region of 10⁻³ AU with respect to the variation of the semi-major axes of Uranus and Neptune. Fictitious planetary systems with initial conditions in this region can undergo systematic variations of semi-major axes. The true Solar System is marginally in this region, and Uranus and Neptune undergo very slow systematic variations of semi-major axes with speed of order 10⁻⁴ AU/Gyr.     

New observational constraints on the temperature inversions of Uranus and Neptune

We present 20-μm photometry of Uranus and Neptune which confirms the presence of a temperature inversion in the lower stratospheres in both planets. We find the brightness temperature difference between 17.8 and 19.6 μm to be 0.8 ± 0.5°K for Uranus and 1.8 ± 0.6°K for Neptune. These results indicate that the temperature inversions on both planets are weaker than previously thought. Comparison to model atmospheres by J. Appleby [Ph.D. thesis, SUNY at Stony Brook 1980] indicates that the temperature inversions can be understood as arising from heating by the absorption of sunlight by CH₄ and aerosols. However, the stratospheric CH₄ mixing ratio on Neptune must be higher than that at the temperature minimum.     

Uranus and Neptune: Shape and rotation

Both Uranus and Neptune are thought to have strong zonal winds with velocities of several 100 m s⁻¹. These wind velocities, however, assume solid-body rotation periods based on Voyager 2 measurements of periodic variations in the planets’ radio signals and of fits to the planets’ magnetic fields; 17.24 h and 16.11 h for Uranus and Neptune, respectively. The realization that the radio period of Saturn does not represent the planet’s deep interior rotation and the complexity of the magnetic fields of Uranus and Neptune raise the possibility that the Voyager 2 radio and magnetic periods might not represent the deep interior rotation periods of the ice giants. Moreover, if there is deep differential rotation within Uranus and Neptune no single solid-body rotation period could characterize the bulk rotation of the planets. We use wind and shape data to investigate the rotation of Uranus and Neptune. The shapes (flattening) of the ice giants are not measured, but only inferred from atmospheric wind speeds and radio occultation measurements at a single latitude. The inferred oblateness values of Uranus and Neptune do not correspond to bodies rotating with the Voyager rotation periods. Minimization of wind velocities or dynamic heights of the 1 bar isosurfaces, constrained by the single occultation radii and gravitational coefficients of the planets, leads to solid-body rotation periods of ∼16.58 h for Uranus and ∼17.46 h for Neptune. Uranus might be rotating faster and Neptune slower than Voyager rotation speeds. We derive shapes for the planets based on these rotation rates. Wind velocities with respect to these rotation periods are essentially identical on Uranus and Neptune and wind speeds are slower than previously thought. Alternatively, if we interpret wind measurements in terms of differential rotation on cylinders there are essentially no residual atmospheric winds.     

Ionospheric models of Saturn,Uranus, and Neptune

Model ionospheres are calculated for Saturn, Uranus, and Neptune. Protons are the major ions above 150 km altitude measured from a reference level where the hydrogen density is 1 × 10¹⁶ molecules cm^?3, while below 150 km quick conversion of protons to H₃⁺ ions by a three-body association mechanism leads to a rapid removal of ionization in dissociative recombination of H₃⁺. Electron density maxima are found at about 260 km for Saturn and Uranus and 200 km for Neptune. Present knowledge of the physical and chemical processes in the atmospheres of these planets suggests that their ionospheres probably will not be Jupiter-like.     

Modelling the Jovian planets by a simple analytical algorithm

This paper models the structures of the Jovian atmospheres and cores by a simple analytical algorithm, which does not require the use of a computer. The method known as the MDV (Motz-Doorish Variable) method was first reported in the Irish Astronomical Journal (1989). It is a method to solve the Stellar Interior Equations (SIE) which dictate the structure of a star and/or the Jovian planets (Bodenheimer, 1986). The results are compared mainly, to the work of Stevenson (1982b) and found to be very agreeable. We include tabulated results of both the atmospheres and cores of Jupiter, Saturn, Uranus, and Neptune.     

The dynamics of inclined Neptune Trojans

We investigated the stable area for fictive Trojan asteroids around Neptune’s Lagrangean equilibrium points with respect to their semimajor axis and inclination. To get a first impression of the stability region we derived a symplectic mapping for the circular and the elliptic planar restricted three body problem. The dynamical model for the numerical integrations was the outer Solar system with the Sun and the planets Jupiter, Saturn, Uranus and Neptune. To understand the dynamics of the region around L ₄ and L ₅ for the Neptune Trojans we also used eight different dynamical models (from the elliptic problem to the full outer Solar system model with all giant planets) and compared the results with respect to the largeness and shape of the stable region. Their dependence on the initial inclinations (0° < i < 70°) of the Trojans’ orbits could be established for all the eight models and showed the primary influence of Uranus. In addition we could show that an asymmetry of the regions around L ₄ and L ₅ is just an artifact of the different initial conditions.     

Infrared radiometry of Uranus and Neptune at 21 and 32 μm

Radiometric measurement of Uranus and Neptune near 21 and 32 μm have been made with filters with widths of 8 and 5 μm, respectively. The observations at 21 μm, made on 1985 June 19 at the NASA Infrared telescope facility at Mauna Kea, Hawaii, were calibrated against α Boo and corresponded to brightness temperatures of 54.1 ± 0.3 K for Uranus and 58.1 ± 0.3 K for Neptune. The observations at 32 μm were made on three nights: 1983 May 1 and 1984 May 30 and 31, also at the NASA IRTF. Calibrated against the Jovian satellites Callisto (J4) and Ganymede (J3), these measurements corresponded to brightness temperatures of 51.8 ± 1.5 K for Uranus and 55.6 ± 1.2 K for Neptune. The observations are consistent with higher-resolution studies and confirm the general decrease of brightness temperatures going from about 20 to 30 μm.     

Generation of equatorial jets by large-scale latent heating on the giant planets

Three-dimensional numerical simulations show that large-scale latent heating resulting from condensation of water vapor can produce multiple zonal jets similar to those on the gas giants (Jupiter and Saturn) and ice giants (Uranus and Neptune). For plausible water abundances (3-5 times solar on Jupiter/Saturn and 30 times solar on Uranus/Neptune), our simulations produce ∼20 zonal jets for Jupiter and Saturn and 3 zonal jets on Uranus and Neptune, similar to the number of jets observed on these planets. Moreover, these Jupiter/Saturn cases produce equatorial superrotation whereas the Uranus/Neptune cases produce equatorial subrotation, consistent with the observed equatorial-jet direction on these planets. Sensitivity tests show that water abundance, planetary rotation rate, and planetary radius are all controlling factors, with water playing the most important role; modest water abundances, large planetary radii, and fast rotation rates favor equatorial superrotation, whereas large water abundances favor equatorial subrotation regardless of the planetary radius and rotation rate. Given the larger radii, faster rotation rates, and probable lower water abundances of Jupiter and Saturn relative to Uranus and Neptune, our simulations therefore provide a possible mechanism for the existence of equatorial superrotation on Jupiter and Saturn and the lack of superrotation on Uranus and Neptune. Nevertheless, Saturn poses a possible difficulty, as our simulations were unable to explain the unusually high speed (∼) of that planet’s superrotating jet. The zonal jets in our simulations exhibit modest violations of the barotropic and Charney-Stern stability criteria. Overall, our simulations, while idealized, support the idea that latent heating plays an important role in generating the jets on the giant planets.     

Multiwavelength Study of a Solar Eruption from AR NOAA 11112 I. Flux Emergence, Sunspot Rotation and Triggering of a Solar Flare

We analyze the multiwavelength observations of an M2.9/1N flare that occurred in the active region (AR) NOAA 11112 in the vicinity of a huge filament system on 16 October 2010. SDO/HMI magnetograms reveal the emergence of a bipole (within the existing AR) 50 hours prior to the flare event. During the emergence, both the positive and negative sunspots in the bipole show translational as well as rotational motion. The positive-polarity sunspot shows significant motion/rotation in the south-westward/clockwise direction, and we see continuously pushing/sliding of the surrounding opposite-polarity field region. On the other hand, the negative-polarity sunspot moves/rotates in the westward/anticlockwise direction. The positive-polarity sunspot rotates ≈?70^° within 30 hours, whereas the one with negative polarity rotates ≈?20^° within 10 hours. SDO/AIA 94 Å EUV images show the emergence of a flux tube in the corona, consistent with the emergence of the bipole in HMI. The footpoints of the flux tube were anchored in the emerging bipole. The initial brightening starts at one of the footpoints (western) of the emerging loop system, where the positive-polarity sunspot pushes/slides towards a nearby negative-polarity field region. A high speed plasmoid ejection (speed ≈?1197 km?s^?1) was observed during the impulsive phase of the flare, which suggests magnetic reconnection of the emerging positive-polarity sunspot with the surrounding opposite-polarity field region. The entire AR shows positive-helicity injection before the flare event. Moreover, the newly emerging bipole reveals the signature of a negative (left-handed) helicity. These observations provide unique evidence of the emergence of twisted flux tubes from below the photosphere to coronal heights, triggering a flare mainly due to the interaction between the emerging positive-polarity sunspot and a nearby negative-polarity sunspot by the shearing motion of the emerging positive sunspot towards the negative one. Our observations also strongly support the idea that the rotation can most likely be attributed to the emergence of twisted magnetic fields, as proposed by recent models.     

The internal structures and the relative rotation rates of Uranus and Neptune

The difference between the interior structures of Uranus and Neptune is presented, based on models which fit the observed mass, radius, and gravitational moments for the assumed rotation periods of these planets. If Uranus and Neptune are assumed to be as similar in internal structure as they are in mass and radius, the rotation period for Neptune must be shorter than that for Uranus. It is suggested that the true rotation period is given by Neptune's oblateness, while the photometric period corresponds to the motion of Rossby waves in the upper atmosphere.     

A Phenomenological Study of the Cosmic Ray Variations over the Past 9400 Years, and Their Implications Regarding Solar Activity and the Solar Dynamo

Two 9400-year long ¹⁰Be data records from the Arctic and Antarctic and a ¹⁴C record of equal length were used to investigate the periodicities in the cosmic radiation incident on Earth throughout the past 9400 years. Fifteen significant periodicities between 40 and 2320 years are observed in the ¹⁰Be and ¹⁴C records, there being close agreement between the periodicities in each record. We found that the periodic variations in the galactic cosmic radiation are the primary cause for periods <?250 years, with minor contributions of terrestrial origin possible >?250 years. The spectral line for the Gleissberg (87-year) periodicity is narrow, indicating a stability of ≈?0.5 %. The 9400-year record contains 26 Grand Minima (GM) similar to the Maunder Minimum, most of which occurred as sequences of 2?–?7 GM with intervals of 800?–?1200 years in between, in which there were no GM. The intervals between the GM sequences are characterised by high values of the modulation function. Periodicities <?150 years are observed in both the GM intervals and the intervals in between. The longer-period variations such as the de Vries (208-year) cycle have high amplitudes during the GM sequences and are undetectable in between. There are three harmonically related pairs of periodicities (65 and 130 years), (75 and 150 years), and (104 and 208 years). The long periodicities at 350, 510, and 708 years closely approximate 4, 6, and 8 times the Gleissberg period (87 years). The well-established properties of cosmic-ray modulation theory and the known dependence of the heliospheric magnetic field on the solar magnetic fields lead us to speculate that the periodicities evident in the paleo-cosmic-ray record are also present in the solar magnetic fields and in the solar dynamo. The stable, narrow natures of the Gleissberg and other periodicities suggest that there is a strong “frequency control” in the solar dynamo, in strong contrast to the variable nature (8?–?15 years) of the Schwabe (11-year) solar cycle.     

The geometric albedos of Uranus and Neptune between 2100 and 3350 Å

Absolutely calibrated spectra of Uranus, Neptune, and the solar analog stars 16 Cyg A and B between 2100 and 3350 Å are reported. The geometric albedos of both planets are close to the curve expected for a semi-infinite Rayleigh-Raman scattering atmosphere between 2100 and 2800 Å. Longward of 2800 Å the albedos fall below the Rayleigh-Raman values and connect smoothly to the ground-based photometry of J.S. Neff, D.C. Humm, J.T. Bergstralh, A.L. Cochran, W.D. Cochran, E.S. Barker, and R.G. Tull (1984, Icarus60, 221–235).Neptune is about 5.5% brighter than Uranus and shows slightly stronger Raman scattering signatures in the MgII lines at 2800 Å in accordance with the results of Neff et al. for the CaII H and K lines. This means that the stratospheric haze on Neptune is thinner than on Uranus. The fact that the Neptunian geometric albedo between 2100 and 2800 Å is so close to the ideal semi-infinite Rayleigh-Raman scattering atmosphere could be exploited for future absolute calibrations of other Solar System objects in this wavelength region.     

The phase diagram of water and the magnetic fields of Uranus and Neptune

The interior of giant planets can give valuable information on formation and evolution processes of planetary systems. However, the interior and evolution of Uranus and Neptune is still largely unknown. In this paper, we compare water-rich three-layer structure models of these planets with predictions of shell structures derived from magnetic field models. Uranus and Neptune have unusual non-dipolar magnetic fields contrary to that of the Earth. Extensive three-dimensional simulations of Stanley and Bloxham (Stanley, S., Bloxham, J. [2004]. Nature 428, 151-153) have indicated that such a magnetic field is generated in a rather thin shell of at most 0.3 planetary radii located below the H/He rich outer envelope and a conducting core that is fluid but stably stratified. Interior models rely on equation of state data for the planetary materials which have usually considerable uncertainties in the high-pressure domain. We present interior models for Uranus and Neptune that are based on ab initio equation of state data for hydrogen, helium, and water as the representative of all heavier elements or ices. Based on a detailed high-pressure phase diagram of water we can specify the region where superionic water should occur in the inner envelope. This superionic region correlates well with the location of the stably-stratified region as found in the dynamo models. Hence we suggest a significant impact of the phase diagram of water on the generation of the magnetic fields in Uranus and Neptune.     

Neptune's rotation period: A correction and a speculation on the difference between photometric and spectroscopic results

An error in the Hayes and Belton (1977), Icarus32, 383–401) estimate of the rotation period of Neptune is corrected. If Neptune exhibits the same degree of limb darkening as Uranus near 4900 Å, the rotation period is 15.4 ± 3 hr. This value is compatible with a recent spectroscopic determination of Munch and Hippelein (1979) who find a period of 11.2_?1.2^+1.8 hr. However, if, as indirect evidence suggests, the law of darkening on Neptune at these wavelengths is less pronounced than on Uranus, then the above estimates may need to be lengthened by several hours. Recent photometric data are independently analyzed and are found to admit several possible periods, none of which can be confidently assumed to be correct. The period of Neptune most probably falls somewhere in the range 15–20 hr. The Hayes-Belton estimate of the period of Uranus is essentially unaffected by the above-mentioned error and remains at 24 ± 4 hr. All observers agree that the rotation period of Uranus is longer than that of Neptune.     

Secular Love numbers of the major planets

Secular Love numbers of the major planets have been determined by solving the first (Dirichlet's) boundary — value problem for the level ellipsoid as the boundary surface. It has been demonstrated that the rotational distortions are responsible for the actual figure of the bodies above. The 6th degree Stokes zonal parameter for Uranus and for Neptune have been predicted.